Some properties of TQFT representations of mapping class groups
Abstract:
I will discuss work done in collaboration with Jørgen Ellegaard Andersen
concerning the projective representations of mapping class groups of surfaces
provided by three-dimensional topological quantum field theory as defined
by Reshetikhin and Turaev. Results from references [1] and [2], showing how
techniques of rational conformal field theory can be used to investigate some
properties of these representations, will be reviewed. Furthermore I will show
how such representations generically carry actions of finite Heisenberg groups,
generalizing the situation for Chern-Simons theory with abelian gauge group.